{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!--BOOK_INFORMATION-->\n",
    "<a href=\"https://www.packtpub.com/big-data-and-business-intelligence/machine-learning-opencv\" target=\"_blank\"><img align=\"left\" src=\"data/cover.jpg\" style=\"width: 76px; height: 100px; background: white; padding: 1px; border: 1px solid black; margin-right:10px;\"></a>\n",
    "*This notebook contains an excerpt from the book [Machine Learning for OpenCV](https://www.packtpub.com/big-data-and-business-intelligence/machine-learning-opencv) by Michael Beyeler.\n",
    "The code is released under the [MIT license](https://opensource.org/licenses/MIT),\n",
    "and is available on [GitHub](https://github.com/mbeyeler/opencv-machine-learning).*\n",
    "\n",
    "*Note that this excerpt contains only the raw code - the book is rich with additional explanations and illustrations.\n",
    "If you find this content useful, please consider supporting the work by\n",
    "[buying the book](https://www.packtpub.com/big-data-and-business-intelligence/machine-learning-opencv)!*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!--NAVIGATION-->\n",
    "< [Discovering Hidden Structures with Unsupervised Learning](08.00-Discovering-Hidden-Structures-with-Unsupervised-Learning.ipynb) | [Contents](../README.md) | [Compressing Color Spaces Using k-Means](08.02-Compressing-Color-Images-Using-k-Means.ipynb) >"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Understanding k-means clustering\n",
    "\n",
    "The most essential clustering algorithm that OpenCV provides is $k$-means clustering, which\n",
    "searches for a predetermined number of $k$ clusters (or groups) within an unlabeled\n",
    "multidimensional dataset.\n",
    "\n",
    "It does so by using two simple assumptions about what an optimal clustering should look\n",
    "like:\n",
    "- The center of each cluster is simply the arithmetic mean of all the points belonging to the cluster\n",
    "- Each point in the cluster is closer to its own center than to other cluster centers\n",
    "\n",
    "It's the easiest to understand the algorithm by looking at a concrete example."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Implementing our first k-means example\n",
    "\n",
    "First, let's generate a 2D dataset containing four distinct blobs. To emphasize that this is an\n",
    "unsupervised approach, we will leave the labels out of the visualization. We will continue\n",
    "using Matplotlib for all our visualization purposes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "plt.style.use('ggplot')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Following the same recipe from earlier chapters, we will create a total of 300 blobs\n",
    "(`n_samples=300`) belonging to four distinct clusters (`centers=4`):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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FiFxpSSnAoCzNSAVAQ81PVSbUpkSmE+xgcooh1mpOJWTFJ5GtLBZ0zQSB4Mm/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\nD2KCAMOAWLrLAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f5b97df9198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.datasets.samples_generator import make_blobs\n",
    "X, y_true = make_blobs(n_samples=300, centers=4,\n",
    "                       cluster_std=1.0, random_state=10)\n",
    "plt.figure(figsize=(10, 6))\n",
    "plt.scatter(X[:, 0], X[:, 1], s=100);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Even without assigning target labels to the data, it is straightforward to pick out the four\n",
    "clusters by eye. The $k$-means algorithm can do this, too, without having any information\n",
    "about target labels or underlying data distributions.\n",
    "\n",
    "Although $k$-means is, of course, a statistical model, in OpenCV, it does not come via the `ml`\n",
    "module and the common train and predict API calls. Instead, it is directly available as\n",
    "`cv2.kmeans`. In order to use the model, we have to specify some arguments, such as the\n",
    "termination criteria and some initialization flags. Here, we will tell the algorithm to\n",
    "terminate whenever the error is smaller than 1.0 (`cv2.TERM_CRITERIA_EPS`) or when ten\n",
    "iterations have been executed (`cv2.TERM_CRITERIA_MAX_ITER`):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import cv2\n",
    "criteria = (cv2.TERM_CRITERIA_EPS + cv2.TERM_CRITERIA_MAX_ITER,\n",
    "            10, 1.0)\n",
    "flags = cv2.KMEANS_RANDOM_CENTERS"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we can pass the preceding data matrix (`X`) to `cv2.means`. We also specify the number\n",
    "of clusters (4) and the number of attempts the algorithm should make with different\n",
    "random initial guesses (10), as shown in the following snippet:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "compactness, labels, centers = cv2.kmeans(X.astype(np.float32), 4,\n",
    "                                          None, criteria, 10, flags)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Three different variables are returned. The first one, `compactness`, returns the sum of\n",
    "squared distances from each point to their corresponding cluster centers. A high\n",
    "**compactness score** indicates that all points are close to their cluster centers, whereas a low\n",
    "compactness score indicates that the different clusters might not be well separated:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "527.01581170992"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "compactness"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Of course, this number strongly depends on the actual values in `X`. If the distances between\n",
    "points were large to begin with, we cannot expect an arbitrarily small compactness score.\n",
    "Hence, it is more informative to plot the data points, colored to their assigned cluster labels:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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OzGMZF7O27iDr6rNp9jjQShoyTLFcHj+FWEPHKRKH7Oo3oyldTfs5nU4++ugj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PAAAW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\n8H8tE8Q8b4TkkwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f5b7e608390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 6))\n",
    "plt.scatter(X[:, 0], X[:, 1], c=labels, s=100)\n",
    "plt.scatter(centers[:, 0], centers[:, 1], c='black', s=200, alpha=0.5);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The good news here is that the $k$-means algorithm (at least in this simple case) assigns the\n",
    "points to clusters very similarly to how we might have, had we done the job by eye. But\n",
    "how did the algorithm find these different clusters so quickly? After all, the number of\n",
    "possible combinations of cluster assignments is exponential to the number of data points!\n",
    "By hand, trying all possible combinations would have certainly taken forever.\n",
    "\n",
    "Fortunately, an exhaustive search is not necessary. Instead, the typical approach that $k$-means\n",
    "takes is to use an iterative algorithm, also known as **expectation-maximization**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Understanding expectation-maximization\n",
    "\n",
    "$k$-means clustering is but one concrete application of a more general algorithm known as\n",
    "expectation-maximization. In short, the algorithm works as follows:\n",
    "1. Start with some random cluster centers.\n",
    "2. Repeat until convergence:\n",
    "   - Expectation step: Assign all data points to their nearest cluster center.\n",
    "   - Maximization step: Update the cluster centers by taking the mean of all the points in the cluster.\n",
    "   \n",
    "Here, the expectation step is so named because it involves updating our expectation of\n",
    "which cluster each point in the dataset belongs to. The maximization step is so named\n",
    "because it involves maximizing a fitness function that defines the location of the cluster\n",
    "centers. In the case of $k$-means, maximization is performed by taking the arithmetic mean of\n",
    "all the data points in a cluster.\n",
    "\n",
    "Refer to the book for step-by-step illustrations on how expectation-maximization works."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Implementing our own expectation-maximization solution\n",
    "\n",
    "The expectation-maximization algorithm is simple enough for us to code it up ourselves. To\n",
    "do so, we will define a function `find_clusters(X, n_clusters, rseed=5)` that takes\n",
    "as input a data matrix (`X`), the number of clusters we want to discover (`n_clusters`), and a\n",
    "random seed (optional, `rseed`). As will become clear in a second, scikit-learn's\n",
    "`pairwise_distances_argmin` function will come in handy:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import pairwise_distances_argmin\n",
    "\n",
    "def find_clusters(X, n_clusters, rseed=5):\n",
    "    # 1. Randomly choose clusters\n",
    "    rng = np.random.RandomState(rseed)\n",
    "    i = rng.permutation(X.shape[0])[:n_clusters]\n",
    "    centers = X[i]\n",
    "    \n",
    "    while True:\n",
    "        # 2a. Assign labels based on closest center\n",
    "        labels = pairwise_distances_argmin(X, centers)\n",
    "        \n",
    "        # 2b. Find new centers from means of points\n",
    "        new_centers = np.array([X[labels == i].mean(0)\n",
    "                                for i in range(n_clusters)])\n",
    "        \n",
    "        # 2c. Check for convergence\n",
    "        if np.all(centers == new_centers):\n",
    "            break\n",
    "        centers = new_centers\n",
    "    \n",
    "    return centers, labels"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can apply our function to the preceding data matrix `X` we created. Since we know what\n",
    "the data looks like, we know that we are looking for four clusters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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xuVZvhNFBsgYtbS24fcpgxGeUoL6H5XfM8ZBJEeDpgi/ikmHsgzIaAFBUrcIv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\nAQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f5bc8123160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "centers, labels = find_clusters(X, 4)\n",
    "plt.figure(figsize=(10, 6))\n",
    "plt.scatter(X[:, 0], X[:, 1], c=labels, s=100);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see, our home-made algorithm got the job done! Granted, this particular\n",
    "clustering example was fairly easy, and most real-life implementations of $k$-means\n",
    "clustering will do a bit more under the hood. But for now, we are happy."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Knowing the limitations of expectationmaximization\n",
    "\n",
    "For its simplicity, expectation-maximization performs incredibly well in a range of\n",
    "scenarios. That being said, there are a number of potential limitations that we need to be\n",
    "aware of:\n",
    "- Expectation-maximization does not guarantee that we will find the globally best solution.\n",
    "- We must know the number of desired clusters beforehand.\n",
    "- The decision boundaries of the algorithms are linear.\n",
    "- The algorithm is slow for large datasets.\n",
    "\n",
    "Let's quickly discuss these potential caveats in a little more detail."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### First caveat: No guarantee of finding the global optimum\n",
    "\n",
    "Although mathematicians have proved that the expectation-maximization step improves\n",
    "the result in each step, there is still no guarantee that, in the end, we will find the global best\n",
    "solution. For example, if we use a different random seed in our simple example (such as\n",
    "using, seed 10 instead of 5), we suddenly get very poor results:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Md0nLVbjSX9uVdAFKE650lr1OnPso6p4UdFdUa38q93iOJDdEaquJI4g21VCqGVpahxah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\nwP8BFeX+wzOA1WUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f5b8c57de80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "centers, labels = find_clusters(X, 4, rseed=10)\n",
    "plt.figure(figsize=(10, 6))\n",
    "plt.scatter(X[:, 0], X[:, 1], c=labels, s=100);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What happened?\n",
    "\n",
    "The short answer is that the random initialization of cluster centers was unfortunate. It led\n",
    "to the center of the yellow cluster migrating in—between the two top blobs, essentially\n",
    "combining them into one. As a result, the other clusters got confused because they suddenly\n",
    "had to split two visually distinct blobs into three clusters.\n",
    "\n",
    "For this reason, it is common for the algorithm to be run for multiple initial states. Indeed,\n",
    "OpenCV does this by default (set by the optional `attempts` parameter)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Second caveat: We must select the number of clusters beforehand\n",
    "\n",
    "Another potential limitation is that $k$-means cannot learn the number of clusters from the\n",
    "data. Instead, we must tell it how many clusters we expect beforehand. You can see how\n",
    "this could be problematic for complicated real-world data that you don't fully understand\n",
    "yet.\n",
    "\n",
    "From the viewpoint of $k$-means, there is no wrong or nonsensical number of clusters. For\n",
    "example, if we ask the algorithm to identify six clusters in the dataset generated in the\n",
    "preceding section, it will happily proceed and find the best six clusters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "criteria = (cv2.TERM_CRITERIA_EPS + cv2.TERM_CRITERIA_MAX_ITER, 10, 1.0)\n",
    "flags = cv2.KMEANS_RANDOM_CENTERS\n",
    "compactness, labels, centers = cv2.kmeans(X.astype(np.float32), 6, None, criteria, 10, flags)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, we used the exact same preceding code and only changed the number of clusters\n",
    "from four to six. We can plot the data points again and color them according to the target\n",
    "labels:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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VNU55tYU9kl/2sYWJY9SDsptvvhm9Xo9SqUSlUvHAAw/0eV6SJJ599ln27NmD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DAAAT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\nkR1gUkZERERkB5iUEREREdmB/wW+jw0pT0OOjAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f5b7e5faac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 6))\n",
    "plt.scatter(X[:, 0], X[:, 1], c=labels, s=100);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since we generated the data ourselves, we know that each data point comes from a total of\n",
    "four distinct clusters. For more complicated data, where we are uncertain about the right\n",
    "number of clusters, there are a few things we could try.\n",
    "\n",
    "First and foremost, there is the **elbow method**, which asks us to repeat the clustering for a\n",
    "whole range of $k$ values and record the compactness value:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "kvals = np.arange(2, 10)\n",
    "compactness = []\n",
    "for k in kvals:\n",
    "    c, _, _ = cv2.kmeans(X.astype(np.float32), k, None, criteria, 10, flags)\n",
    "    compactness.append(c)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This will result in a plot that looks like an *arm*. The point that lies at the *elbow* is the number\n",
    "of clusters to pick:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7f5b7a5dd160>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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zZk/fCG2/wSp2RUREFPw8nokrLi5GQoLyasTBgwfjwoULzd4UBRaRdJeycDAb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\ngAcR4gAAADyIEAcAAOBBPwEiBiGUXjp1qgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f5b7a5ed780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 6))\n",
    "plt.plot(kvals, compactness, 'o-', linewidth=4, markersize=12);\n",
    "plt.xlabel('number of clusters')\n",
    "plt.ylabel('compactness')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In our case, we would pick the number four. The reasoning behind this is that moving from\n",
    "left to right, four is the smallest number of clusters that gives a very compact representation.\n",
    "Three clusters give us a representation that is only half as compact as four clusters.\n",
    "Choosing five clusters or more does not further improve the compactness. Thus, four\n",
    "should be our best guess as to the number of clusters.\n",
    "\n",
    "A list of more sophisticated methods is given in the book."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Third caveat: Cluster boundaries are linear\n",
    "\n",
    "The $k$-means algorithm is based on a simple assumption, which is that points will be closer\n",
    "to their own cluster center than to others. Consequently, $k$-means always assumes linear\n",
    "boundaries between clusters, meaning that it will fail whenever the geometry of the clusters\n",
    "is more complicated than that.\n",
    "\n",
    "We see this limitation for ourselves by generating a slightly more complicated dataset.\n",
    "Instead of generating data points from Gaussian blobs, we want to organize the data into\n",
    "two overlapping half circles. We can do this using scikit-learn's `make_moons`. Here, we\n",
    "choose 200 data points belonging to two half circles, in combination with some Gaussian\n",
    "noise:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.datasets import make_moons\n",
    "X, y = make_moons(200, noise=.05, random_state=12)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This time, we tell $k$-means to look for two clusters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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VFPIL8mv1/371xxs5E+24iXnSiWR+/WQ1I2+81On55N9w3cj9qxu5f3XT1O9feLhrO8gb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SqtC54UIZisk9WTjCfJZCxqKeIJgubtbptQf7ZjE+rSHse080USPEdQNqSdEO5Jqs7aoQlZJ2Mg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\nNClTSimllMoDmpQppZRSSuWB/w+3lq5zFBkkvwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f5b8c56d518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "criteria = (cv2.TERM_CRITERIA_EPS + cv2.TERM_CRITERIA_MAX_ITER, 10, 1.0)\n",
    "flags = cv2.KMEANS_RANDOM_CENTERS\n",
    "compactness, labels, centers = cv2.kmeans(X.astype(np.float32), 2, None, criteria, 10, flags)\n",
    "plt.figure(figsize=(10, 6))\n",
    "plt.scatter(X[:, 0], X[:, 1], c=labels, s=100);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As is evident from the plot, $k$-means failed to identify the two half circles and instead split\n",
    "the data with what looks like a diagonal straight line (from bottom left to top right).\n",
    "\n",
    "This scenario should ring a bell. We had the exact same problem when we talked about\n",
    "linear SVMs in [Chapter 6](06.00-Detecting-Pedestrians-with-Support-Vector-Machines.ipynb), *Detecting Pedestrians with Support Vector Machines*. The idea there\n",
    "was to use the kernel trick in order to transform the data into a higher-dimensional feature\n",
    "space. Can we do the same here?\n",
    "\n",
    "We most certainly can. There is a form of kernelized k-means that works akin to the kernel\n",
    "trick for SVMs, called **spectral clustering**. Unfortunately, OpenCV does not provide an\n",
    "implementation of spectral clustering. Fortunately, scikit-learn does:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.cluster import SpectralClustering"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The algorithm uses the same API as all other statistical models: We set optional arguments\n",
    "in the constructor and then call `fit_predict` on the data. Here, we want to use the graph\n",
    "of the nearest neighbors to compute a higher-dimensional representation of the data and\n",
    "then assign labels using $k$-means:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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zlLLMI9fPR6O+TiGlH8HmLBpjirHHlxNUhEeokp/hyuZer4d4mSz30aTXwQD2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NAAAg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\nCCEcQEEZIYQQQggH/D+KmpX/gPXdDwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f5b77b14c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = SpectralClustering(n_clusters=2, affinity='nearest_neighbors',\n",
    "                           assign_labels='kmeans')\n",
    "labels = model.fit_predict(X)\n",
    "plt.figure(figsize=(10, 6))\n",
    "plt.scatter(X[:, 0], X[:, 1], c=labels, s=100);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that spectral clustering gets the job done. Alternatively, we could have transformed\n",
    "the data into a more suitable representation ourselves and then applied OpenCV's linear $k$-means\n",
    "to it. The lesson of all this is that perhaps, again, feature engineering saves the day."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fourth caveat: k-means is slow for a large number of samples\n",
    "\n",
    "The final limitation of $k$-means is that it is relatively slow for large datasets. You can\n",
    "imagine that quite a lot of algorithms might suffer from this problem. However, $k$-means is\n",
    "affected especially badly: each iteration of $k$-means must access every single data point in\n",
    "the dataset and compare it to all the cluster centers.\n",
    "\n",
    "You might wonder whether the requirement to access all data points during each iteration\n",
    "is really necessary. For example, you might just use a subset of the data to update the\n",
    "cluster centers at each step. Indeed, this is the exact idea that underlies a variation of the\n",
    "algorithm called batch-based k-means. Unfortunately, this algorithm is not implemented in\n",
    "OpenCV.\n",
    "\n",
    "Despite the limitations discussed earlier, $k$-means has a number of interesting applications,\n",
    "especially in computer vision."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!--NAVIGATION-->\n",
    "< [Discovering Hidden Structures with Unsupervised Learning](08.00-Discovering-Hidden-Structures-with-Unsupervised-Learning.ipynb) | [Contents](../README.md) | [Compressing Color Spaces Using k-Means](08.02-Compressing-Color-Images-Using-k-Means.ipynb) >"
   ]
  }
 ],
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   "language": "python",
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   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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